Let N be a six digit number with distinct digits. Find the number N given that the numbers N, 2N, 3N, 4N, 5N, 6N, when written underneath each other, form a latin square (that is each row and each column contains all six digits).

What a Joke

Stage: 4 Challenge Level:

The first hint is very helpful - and understanding inverses important.

The factorisation is subtle and this is where the problem makes a *** challenge level, possibly easy to acceptonce told but hard to be sure there is understanding.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.